Statistocal Modeling of Lapped Transforma Coefficients and its Applications : Statistical Modeling of Lapped Transform Coefficients and its applications

Abstract

In the last two decades, statistical modeling in wavelet domain has been an active research area due to its multiresolution and time frequency localization properties. These properties have been effciently exploited in many image processing applications like image compression, denoising, deblocking, deblurring etc with considerable success. The main drawback of wavelet transform is that it is not very good in capturing the directional information present in natural images. The Lapped Transforms have been proposed to overcome the blocking artifacts of the DCT with increased coding gain. It was observed that the Lapped Transforms (LT) based methods are very good in preserving oscillatory components present in images like textures. This thesis deals with statistical modeling of LT coefcients of natural images and its applications. The thesis first considers an exhaustive study on the determination of a suitable statistical distribution that best approximates the block Lapped Orthogonal Transform (LOT) and Lapped Bi-orthogonal Transform (LBT) coefcients. The widely used Kolomogrov-Smirnov (KS) and Chisquare goodness of it tests indicate that the Generalized Gaussian is the most appropriate statistical distribution that best approximates the block LOT and LBT coefcients of natural images. Such a study is very useful in the design of optimal quantizers that may lead to minimum distortion. Employing the dyadic remapping feature of LTs, the LT coefcients can be rearranged into octave-like representation. The rearranged LT coefcients in various detailed subbands show highly non Gaussian statistics and can be modeled in a way similar to wavelet coefcients. The dyadic remapped LT coefcients when used in compression and denoising applications show performance comparable to that of wavelet based methods. This thesis next considers an exhaustive study on the determination of a suitable statistical distribution that best models the dyadic remapped LT coefcients. The experimental results indicate that the Generalized Gaussian distribution best approximates the dyadic remapped LT coe cients. Such a study plays an important role in developing more e cient algorithms for compression and denoising applications. The problem of reducing additive white Gaussian noise in LOT domain is considered in the thesis. The main motivation is that LOT has good energy compaction, it is robust to oversmoothing and the noise and the signal statistics can be modeled precisely in the LT domain. We propose three LT based image denoising methods based on statistical modeling of dyadic rearranged LT coe cients. The rst method uses a Bayesian minimum mean square error (MMSE) estimator based on modeling the global distribution of dyadic rearranged LT coe cients by Generalized Gaussian distribution. The second method assumes the local distribution of the rearranged LT coe cients to be Gaussian with spatially varying variance and applies local Wiener lter to reduce the noise. Based on the encouraging performance of single local Wiener ltering in LT domain, a doubly local Wiener ltering framework is developed in the same domain. The third method employs a maximum a posteriori (MAP) estimator which uses the local Laplace probability density function with local variance for the estimation of the noise free coe cients. Experiment....